Not much to add here except...
In the US, the instructor signs off on every flight that is taken with...him in an instructional role. Sig to include cert no and exp date. I would assume it's the same where you are, which makes me wonder why they didn't sign it.
As for Tip-x, My understanding is that if you change a legal document, you have to cross it out and can't use correction fluid. Not that it really matters of course.